In coherent processing systems such as optical correlators, a laser or other coherent source is typically employed to be modulated in either phase or amplitude by one or more spatial light modulator (SLM) devices. These typically incorporate liquid crystal devices but may also be micromirror microelectromechanical (MEMs) devices. Optical correlator devices are typically used as optical pattern recognition systems, such as the systems described in EP1546838 (WO2004/029746) and EP1420322 (WO99/31563). Both of these prior art documents are incorporated by reference, in a 4f Matched Filter or Joint Transform Correlator (JTC) system, the SLM devices are addressed with functions that represent either input or reference patterns (which can be images) and/or filter patterns, usually based upon Fourier transform representations of reference functions/patterns that are to be “matched” to the input function.
Another coherent free space optical system that uses a similar architecture is the optical derivative processor that is described in EP2137590 (WO2008/110779). This prior art document is incorporated by reference. This employs specific filters to produce derivatives of the input function displayed on an input SLM. It is usual for the optical system to contain one or multiple focussing elements, such as lenses or curved mirrors, in order to produce the Optical Fourier Transform (OFT) of the function represented on the SLM. This is achieved when collimated light is illuminated on an SLM, with the SLM positioned in the front focal plane of the focussing element. The OFT is then produced at the rear focal plane of the focussing element, where either a camera or subsequent SLM is positioned. Other focussing elements that may be used include static diffractive optical elements, typically in the form of zone plates.
A camera such as a complementary metal-oxide-semiconductor (CMOS) sensor is typically positioned in the output plane of the optical system to capture the resulting optical intensity distribution, which in the case of an optical correlator system may contain localised correlation intensities denoting the similarity and relative alignment of the input and references functions. In the case of the optical derivative system, the camera would capture the resulting derivative of the input function.
Such optical systems, especially the 4f matched filter type of correlators suffer from high alignment tolerances, where the pixels of the input SLM must be spatially aligned to coincide with the pixels in the following SLM that may be positioned in the Fourier plane. Three prior art specific embodiments will now be described.
The most common function used in the type of coherent optical systems concerning both the prior art and the invention is the optical Fourier Transform (OFT) the decomposition of a spatial or temporal distribution into its frequency components. This is analogous to the pure form of the two-dimensional Fourier transform denoted by the following equation:
                              G          ⁡                      (                          u              ,              v                        )                          =                              FT            ⁡                          [                              g                ⁡                                  (                                      x                    ,                    y                                    )                                            ]                                =                                    ∫              ±                                                                    ⁢                                          ∫                ∞                                                                              ⁢                                                g                  ⁡                                      (                                          x                      ,                      y                                        )                                                  ⁢                                  exp                  ⁡                                      [                                                                  -                        i                                            ⁢                                                                                          ⁢                      2                      ⁢                                              π                        ⁡                                                  (                                                      ux                            +                            vy                                                    )                                                                                      ]                                                  ⁢                d                ⁢                                                                  ⁢                x                ⁢                                                                  ⁢                d                ⁢                                                                  ⁢                y                                                                        (        1        )            
Where: x,y=space/time variables, u,v=frequency variables
The OFT may be achieved by the optical system shown in FIG. 1 where collimated coherent light of wavelength λ (typically laser light) 1 is modulated in phase or amplitude by a Spatial Light Modulator 2 (typically a liquid crystal or electro-mechanical MEMs array). The modulated beam is then passed through a positive converging lens 3, of focal length f and focussed in the back focal plane of the lens, where a detector such as a CMOS array 4 is positioned to capture the intensity of the resulting Fourier transform.
In optical processing systems, the OFT may be employed as a direct replacement of the electronic/software-based Fast Fourier Transform (FFT) family of algorithms, offering significant advantages in terms of process time and resolution. This process may be used as the basis of a variety of functions. The two functions of primary concern in this application are optical correlation (used in pattern recognition, comparison, or analysis) and derivative calculations.
Correlation between two or more functions may be achieved in an optical system in two main ways, either by a Matched Filter process, denoted by the following equation:r(x,y)*g(x,y)=FT[R(u,y)*×G(u,v)]  (2)
Where upper case functions represent the Fourier transform of their lower case equivalents; “*” indicates the complex conjugate of the adjacent function and “*” denotes the correlation function.
Or by a Joint Transform Correlation process, such as the 1/f JTC described in EP1546838 (WO2004/029746).
In each case the correlation is formed as the inverse Fourier transform of the product of two functions, which have themselves been Fourier transformed. This also forms the basis of how spectral derivative operations may be realised optically, as described in EP2137590 (WO2008/110779), using the following relationship:g′(x,y)=FT[(i2πuv)nG(u,v)]  (3)
Where g′(x,y)=derivative of function g(x,y) of order n
FIG. 2 shows a “4f” optical system that can be used to realise a matched filter or derivative process. Figure shows a collimated coherent light 5 of wavelength λ which is modulated by SLM pixel array 6, and then transmitted through lens 7 and focussed on the second SLM pixel array 8, forming the OFT of the function displayed on the first SLM, at the pixels of the second SLM 8. The resulting optical matrix multiplication is then the inverse Fourier transformed by lens 9 and the result is captured at the detector array 10.
For a matched filter process, the pattern displayed by the pixels of the first SLM 6 will be the “input scene” g(x,y) and the pattern displayed on the second SLM 8 will represent a version of the Fourier transform of the reference function r(x,y).
For a derivative process, the pattern displayed by the second SLM 8 will be the complex function (i2πuv) from equation (3). This may be represented by a combination of phase and amplitude patterns, as described in EP2137590 (WO2008/110779).
A recognised problem in the physical realisation of such optical systems, is the high spatial alignment criteria of the input and filter patterns displayed on the spatial light modulator components, together with the accurate positioning of the other system components, such as lenses and polarisers, etc. These tolerances may be of the order of a few microns, given that the pixel sizes for modern liquid crystal SLMs are of the order of 9 microns. Several methodologies have been proposed to alleviate these high tolerances in order to create optical systems that are both practically achievable and resistant to mechanical noise, vibration and shock, as well as gradual misalignment due to such factors as device and environmental temperature variations. Such solutions include folding the optical path to reduce both the overall size of the system as well as to reduce the number of discreet components required (such as the joint transform correlator (JTC) embodiment in patent EP2137590 (WO2008/110779)) and to replace the positive converging lenses with curved mirrors and static diffraction gratings such as zone plates. Extending the use of the spatial light modulator array to incorporate multiple data input patterns and placing the SLM on the same back plane as the detector array has also been proposed.
FIG. 3 shows such a folded arrangement, where a 4f-type system is outlined. Collimated coherent light 11 is employed as before as the information medium being transmitted through the optical system. The input in SLM 12 and reference/filter SLM 14 are now in the same plane as the detector array 16 and both SLMs are now considered as reflective devices (e.g. pixel arrays mounted upon a plane mirror). The lenses of FIG. 2 are now replaced by two reflective components 13, and 15, either as diffractive optical elements or positive curved mirrors, of focal length f.
However, the principles of the optical processing functions defined above have the potential to create extended processes, such as partial differential equation solving. An example of this is in the field of computational fluid dynamics (CFD), which is governed by the Navier-Stokes (NS) equations. These describe how the motion of a fluid may be determined by the forces acting upon it. Solving such a process by direct numerical simulation is a highly processor intensive operation with high resolution examples being known to take weeks or even months to perform on the world's most powerful processor arrays and supercomputers. Indeed, it is a well-known problem that the serial nature of electronic processing is a fundamental limitation on the size and speed at which such processes may be performed, since the Fast Fourier transform operations that form the basis of such electronic processors are inherently parallel and do not scale well in terms of process time versus resolution. This is in addition to the amounts of data that must be managed to produce the operations. Furthermore, such processors produce overwhelming amounts of flow data (e.g. gigabytes) that must be sampled and discarded, or analysed over impractical amounts of time.
A form of the NS equations are shown in equation (4) below, in one dimensional form.
                                                                                          ρ                  ⁡                                      (                                                                                            ∂                          u                                                                          ∂                          t                                                                    +                                              u                        ⁢                                                                              ∂                            u                                                                                ∂                            x                                                                                              +                                              v                        ⁢                                                                              ∂                            u                                                                                ∂                            y                                                                                              +                                              w                        ⁢                                                                              ∂                            u                                                                                ∂                            z                                                                                                                )                                                  =                                                      -                                                                  ∂                        p                                                                    ∂                        x                                                                              +                                      μ                    ⁡                                          (                                                                                                                                  ∂                              2                                                        ⁢                            u                                                                                ∂                                                          x                              2                                                                                                      +                                                                                                            ∂                              2                                                        ⁢                            u                                                                                ∂                                                          y                              2                                                                                                      +                                                                                                            ∂                              2                                                        ⁢                            u                                                                                ∂                                                          z                              2                                                                                                                          )                                                        +                                      ρ                    ⁢                                                                                  ⁢                                          g                      x                                                                                                                                                                ρ                  ⁡                                      (                                                                                            ∂                          v                                                                          ∂                          t                                                                    +                                              u                        ⁢                                                                              ∂                            v                                                                                ∂                            x                                                                                              +                                              v                        ⁢                                                                              ∂                            v                                                                                ∂                            y                                                                                              +                                              w                        ⁢                                                                              ∂                            v                                                                                ∂                            z                                                                                                                )                                                  =                                                      -                                                                  ∂                        p                                                                    ∂                        y                                                                              +                                      μ                    ⁡                                          (                                                                                                                                  ∂                              2                                                        ⁢                            v                                                                                ∂                                                          x                              2                                                                                                      +                                                                                                            ∂                              2                                                        ⁢                            v                                                                                ∂                                                          y                              2                                                                                                      +                                                                                                            ∂                              2                                                        ⁢                            v                                                                                ∂                                                          z                              2                                                                                                                          )                                                        +                                      ρ                    ⁢                                                                                  ⁢                                          g                      y                                                                                                                                                                ρ                  ⁡                                      (                                                                                            ∂                          w                                                                          ∂                          t                                                                    +                                              u                        ⁢                                                                              ∂                            w                                                                                ∂                            x                                                                                              +                                              v                        ⁢                                                                              ∂                            w                                                                                ∂                            y                                                                                              +                                              w                        ⁢                                                                              ∂                            w                                                                                ∂                            z                                                                                                                )                                                  =                                                      -                                                                  ∂                        p                                                                    ∂                        z                                                                              +                                      μ                    ⁡                                          (                                                                                                                                  ∂                              2                                                        ⁢                            w                                                                                ∂                                                          x                              2                                                                                                      +                                                                                                            ∂                              2                                                        ⁢                            w                                                                                ∂                                                          y                              2                                                                                                      +                                                                                                            ∂                              2                                                        ⁢                            w                                                                                ∂                                                          z                              2                                                                                                                          )                                                        +                                      ρ                    ⁢                                                                                  ⁢                                          g                      x                                                                                                                                       (        4        )            
As can be noticed from the above equations, the building blocks of such equation solvers are analogous to those spectral derivative functions described above. Hence, if the functionality of the optical systems described above may be extended by incorporating multiple mathematical functions, there is the potential to provide step changing advantages, in terms of processing speed, resolution increases, data management and also electrical power consumption. Furthermore, optical correlation-based processing may also provide the means to analyse the currently overwhelming amounts of data being produced by the solver system.
However, practically realising such optical systems is unrealistic due to the alignment and tolerances of the physical components as described above.
The invention seeks to address at least some of the following problems:                the limitations of strict tolerances in rotation and translation of the prior art configurations;        the alignment problems of optical elements;        the inflexibility of the system in responding to changes in environmental conditions;        the overly complex and oversized prior art configurations;        the inability in practical terms of handling large processing tasks;        problems arising from optical crosstalk;        highly restrictive spatial alignment criteria; and        susceptibility to mechanical noise, vibration and shock, as well as gradual misalignment due to such factors as device and environmental temperature variations.        